Question

The probability that a single radar station will detect an enemy plane is 0.65. (a) How many such stations are required to be 98% certain that an enemy plane flying over will be detected by at least one station?

Answer 1

Answer:

4 stations

Step-by-step explanation:

If we need to be at least 98% certain that an enemy plane flying over will be detected by at least one station, we must ensure that there is at most a 2% chance that no radar stations detect the plane.

The probability that a single radar station does not detect the plane is 0.35.

For n radar stations:

$P=0.02=0.35^n\\n=\frac{log(0.02)}{log(0.35)}\\n=3.73$

Rounding up to the next whole station, at least 4 stations are needed.